Solve: 2/7 + 1/2 - 7/14 Fraction Operation Challenge

Question

Solve the following exercise:

27+12714=? \frac{2}{7}+\frac{1}{2}-\frac{7}{14}=\text{?}

Video Solution

Step-by-Step Solution

To solve the expression 27+12714 \frac{2}{7} + \frac{1}{2} - \frac{7}{14} , we need to add and subtract fractions, which requires a common denominator.

  • Step 1: Identify the denominators and find the least common denominator (LCD):
    • The denominators are 7, 2, and 14.
    • The LCM of 7, 2, and 14 is 14.
  • Step 2: Convert each fraction to have the denominator 14:
    • 27=2×27×2=414 \frac{2}{7} = \frac{2 \times 2}{7 \times 2} = \frac{4}{14}
    • 12=1×72×7=714 \frac{1}{2} = \frac{1 \times 7}{2 \times 7} = \frac{7}{14}
    • 714 \frac{7}{14} is already in the form with denominator 14.
  • Step 3: Perform the operations using the common denominator:
    • Add the first two fractions: 414+714=1114 \frac{4}{14} + \frac{7}{14} = \frac{11}{14}
    • Subtract the third fraction: 1114714=414 \frac{11}{14} - \frac{7}{14} = \frac{4}{14}
  • Step 4: Simplify the result if necessary:
    • 414 \frac{4}{14} is already simplified to its simplest form.

Therefore, the solution to the expression 27+12714 \frac{2}{7} + \frac{1}{2} - \frac{7}{14} is 414 \frac{4}{14} , which matches choice 3.

Answer

414 \frac{4}{14}